Permutation Notation

A common notation used in Abstract Algebra.

Permutation of 3 Entries

• $(ijk)$ means:
  • $i$-th entry moves to $j$-th entry
  • $j$-th entry moves to $k$-th entry
  • $k$-th entry moves to $i$-th entry

Single Swap

• $(ij)$ := swap $i$ and $j$

Chain of Swaps

• $(kl)(ij)$ := swap $i$ and $j$ and then swap $k$ and $l$